curve #6225

y² = x³ − 418464273533022561600x + 3181388851150740405986703395625

a-invariants: [0, 0, 0, -418464273533022561600, 3181388851150740405986703395625]
c-invariants: [20086285129585082956800, -2748719967394239710772511733820000]
rank (lower bound): ≥ 18
torsion subgroup: trivial
conductor (N): 1567581293349947783994749296439193923282574541207129862100
discriminant (Δ): 317435211903364426258936732528936769464721344594443797075250000
Faltings height: 10.7601
naive height: 154.0630
primes of bad reduction: 2, 3, 5, 15541, 122891, 1141061, 799244510583326912489117964790746675559
regulator: 170399434163530104.45311690529969528391453973100436297924835488143880276790
submitted by: apkorte
submitted at: 2026-10-31 08:02:51 UTC
last updated: 2026-10-31 08:02:51 UTC

(7808344590, -624461599573425)
(48644695200, 9896139347496525)
(9287100306, 309973749279129)
(9573114900, 229577621037075)
(18860046150, 1413392034405825)
(32923755024, -5009237103548493)
(-22437185700, -1129184484814125)
(-4496189310, 2229795898251975)
(1141362150, 1644766375298175)
(20345286894, -1757598353587953)
(44293342110, 8458446806945775)
(3415220215, 1338684207865300)
(14643727440, 440107648872525)
(8031114360, -581937828772275)
(-11177250936, -2542102396649037)
(662562450, 1704236190927975)
(9267065700, -315110613775725)
(2504865487665/4, 3962302110843758775/8)

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